The height of the BM, drawn from the apex of the rhombus angle ABCD, forms an angle of 30 ° AM = 4cm

The height of the BM, drawn from the apex of the rhombus angle ABCD, forms an angle of 30 ° AM = 4cm with the side AB. Find the length of the diagonal BD of the rhombus if point M lies on the side AD

Since, according to the condition, BM is the height of the rhombus, then the ABM triangle is rectangular, in which the ABM angle is 30.

Then the length of the hypotenuse AB is equal to two lengths of the leg AM.

AB = 2 * AM = 2 * 4 = 8 cm.

Since all the edges of the rhombus are equal, then AD = AB = 8 cm, and the AED triangle is isosceles.

Angle BAD = BAM = (180 – 90 – 30) = 60.

Then the triangle ABD is equilateral, and therefore BD = AB = AD = 8 cm.

Answer: The length of the VD diagonal is 8 cm.